English: “That you may eat” — It was taught: Rabbi says: It is revealed and known before Him Who spoke and the world came into being that unclean animals are more numerous than clean ones; therefore the verse enumerated the clean ones. And it is revealed and known before Him that clean birds are more numerous than unclean ones; therefore the verse enumerated the unclean ones — to teach you that a person should always teach his student the shorter way.
On the daf / in context: The Torah chooses the shorter list in each case so that the student is taught in the most concise manner.
Type of Learning
Derash on the verse (Chullin) — pedagogical preference for the shorter enumeration.
What Is Learned
The Torah enumerates the smaller group (clean animals or unclean birds) so that the student is taught the shorter route.